I finished my last entry expressing my perplexity by the ‘solution’ mathematicians offered six decades ago to the problem of the continuum : Cohen’s theorem according to which both the assumption that there is some set (say, C) larger than the set of natural numbers but smaller than the set of real numbers, and the […]
Infinity has always been one of the most fascinating and perplexing concepts in mathematics. For ancient Greek mathematicians, it was (in a similar way to the notion of zero) something like a non-concept, i.e., something that one was not allowed to think, and only might express and use by means of circumloquia at the best […]
Author: Karen K. Christensen-Dalsgaard, Assistant Professor, Department of Biological Sciences, MacEwan University In the 11th century in Cairo, the foundations for modern science were laid through the detention of an innocent man. The mathematician Abu Ali al-Hasan Ibn al-Haytham had been tasked with regulating the flow of the Nile, but when he saw the river […]
I shall end this series on the problem of verisimilitude by sketching the main methodological norms that can be derived from our favorite definition of “empirical truthlikeness” –remember: the verisimilitude of a hypothesis H on the light of the empirical data E, or Vs(H,E ), would be equivalent to p(H,E)/p(HvE). Remember as well that by […]
In the previous entry I introduced my definition of a concept of empirical verisimilitude of a proposition H given the evidence E (or how close to the truth H seems under the light of data E), Vs(H,E) , as the combination of the similarity or coherence between H and E, and that between E and […]
For the problem of scientific realism, the most consequential implication of the ‘ugly duckling theorem’ we met in our last entry was that judgments of similarity seem to be not reducible to any kind of algorithmic definition that might tell in an objective way how much ‘similar’ is one thing to another, for these judgments […]
As we saw in my last entry, Karl Popper suggested around 1960 a way of formalising the idea that science can proceed towards the (full) truth through a series of theories or hypotheses all of which are literally false. Basically, his proposal was to define the relation of ‘theory A being at least as close […]
Probably, the most common assumption about scientific knowledge amongst the general public, and certainly amongst a substantial percentage of the philosophers of science, is that science attempts to find out the truth about the world (just like many other institutions or professions, like the courts, the police or whoever that needs to look for information […]
Author: Alexander V. Gheorghiu, Research Fellow in Logic or Applied Logic, University College London The rigid structures of language we once clung to with certainty are cracking. Take gender, nationality or religion: these concepts no longer sit comfortably in the stiff linguistic boxes of the last century. Simultaneously, the rise of AI presses upon us […]
The idea of the countless “virtual worlds” that the metaverse will contain is, as we saw in our last entry, an extrapolation of the idea of “video game worlds,” not necessarily regarding their playful nature—since the metaverse is expected to be a place for almost any kind of activity, not just leisure—but in the sense […]